I was wondering the difference between norm and distance. My teacher told me that a norm always induce a distance, but that the reciprocal is not true. So, let $(E,\|\cdot \|)$ a normed space. I agree that we can give a structure of metric space by setting $d(x,y)=\|x-y\|$. Now let $(E,d)$ a metric space. Why $\|x\|=d(x,0)$ would not be a norm over $E$ ?
2026-04-13 19:44:21.1776109461
Difference between norm and distance.
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